NCAFM2023 Programme Booklet

REAL-SPACE DFT SIMULATION OF ENERGY DISSIPATION DUE TO ATOMIC DISPLACEMENTS OF A Si TIP AND A Si(111)-(7×7) SURFACE DETECTED BY NC-AFM

Toyoko Arai 1* , Jun-Ichi Iwata 2 , Atsushi Oshiyama 3 , Masahiko Tomitori 4

1 Graduate school of Natural Science and Technology, Kanazawa University, 920-1192 Japan 2 Institute of Innovative Research, Tokyo Institute of Technology, 152-8550 Japan 3 IMaSS, Nagoya University, 464-8601 Japan 4 Japan Advanced Institute of Science and Technology, 923-1292, Japan

Email: arai@staff.kanazawa-u.ac.jp

In the last two decades the conservative and non-conservative (dissipative) force interactions between a tip and a sample in proximity have been intensively examined by non-contact atomic force microscopy (nc-AFM). The channel of nc-AFM to measure the energy dissipation through the non-conservative force interactions has been regarded to have great potential to explore nano-mechanical phenomena. We had experimentally found that, when the nc-AFM image showed the high resolution for the individual adatoms on a Si(111)-(7×7) surface, the simultaneously obtained energy dissipation signal increased in close proximity over the hollow sites surrounded by a Si adatom and a Si rest atom with a dangling bond per each [1]. In this study, to elucidate the mechanism of increase in dissipation, the forces between a Si tip and a Si(111)-(7×7) surface were calculated using real-space density functional theory (RSDFT) [2]. RSDFT is a first-principles program developed by Oshiyama and Iwata, which uses a real-space difference method and a pseudopotential method. First, we optimized the structure of a Si(111)-(7×7) reconstructed surface and the structure of a [001]-oriented Si dimer tip [3] by RSDFT. Next, we calculated the structure changes and the forces acting between the tip and the Si surface during tip approaching and retracting over the hollow site; the separation between the tip apex atom and the Si adatom on the surface was varied from 5.0 to 2.0 Å, as shown in the figure. The atom structure and the force-distance curve exhibited hysteresis along with the tip travel. The greyed area surrounding by the force-distance curve corresponds to the nonconservative dissipation energy, which could be experimentally measured. Notably, the calculations with a Si(111)-(7×7) surface with H-terminated rest atoms or H-terminated adatom did not show such hysteresis during one cycle of the tip travel. This calculation for the hydrogen termination was also in good agreement with the experiment.

Fig. Force–distance curve with the optimized structures of the Si tip and Si(111)-(7×7) surface, calculated by RSDFT.

References [1] T. Arai, R. Inamura, D. Kura, and M. Tomitori, Phys. Rev. B, 2018, 97 , 115428. [2] J.-I. Iwata, D. Takahashi, A. Oshiyama, et al., J. Comput. Phys., 2010, 229 , 2339. [3] P. Pou, S. A. Ghasemi, P. Jelinek, T. Lenosky, S. Goedecker, and R. Perez, Nanotechnology, 2009, 20 , 264015.

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